(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

How does the gauge transformation

[itex]A\rightarrow A +\nabla \Psi(r,t) \\

\phi \rightarrow \phi - \frac{1}{c}\frac{\partial \Psi}{\partial t}[/itex]

change the Lagrangian and the motion of a single particle moving in an electromagnetic field.

2. Relevant equations

The Lagrangian before the transformation

[itex]L=\frac{1}{2}mv^{2} -q\phi + q A\cdot v[/itex]

3. The attempt at a solution

I get to a solution that looks like

[itex]L' =\frac{1}{2}mv^{2} -q\phi + q A\cdot v + q\frac{d\Phi}{dt} + q\left(\frac{1}{c}-1\right)\frac{\partial \Phi}{\partial t}[/itex]

the factor of 1/c could be the problem. I cannot see the motion of the particle changing because of the transformation and I know that the lagrangian can be changed by the time derivative of a function without changing the equations of motion. However because of the factor I still have partial time derivatives left in the solution which troubles me. Anyone know what could be wrong?

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# Homework Help: Lagrangian under transformation

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